Classical field theory. Advanced mathematical formulation

TL;DR

This paper discusses the advanced mathematical formulation of classical field theory using fibre bundles, graded manifolds, and jet manifolds, and explores its BRST extension for quantization.

Contribution

It introduces a rigorous mathematical framework for classical field theory and extends it via BRST methods for quantization.

Findings

Mathematical formulation of classical field theory using fibre bundles and jet manifolds

Application of second Noether theorems to derive BRST extension

Framework facilitates the quantization process of classical fields

Abstract

In contrast with QFT, classical field theory can be formulated in strict mathematical terms of fibre bundles, graded manifolds and jet manifolds. Second Noether theorems provide BRST extension of this classical field theory by means of ghosts and antifields for the purpose of its quantization.